We compare two methods for analyzing periodic dimer models. These are the
matrix-valued orthogonal polynomials approach due to Duits and one of the authors, and
the Wiener–Hopf approach due to Berggren and Duits. We establish their equivalence
in the special case of the Aztec diamond. Additionally, we provide explicit formulas
for the matrix-valued orthogonal polynomials/Wiener–Hopf factors in the case of the
-periodic
Aztec diamond in terms of Jacobi theta functions related to the spectral curve of
the model.
